Subgroups — C₂₉×D₅₄₉ #44541540

Order 31842.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₂₉×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂₉×D₁₈₃	—	3	1	no	maximal
3	C₃×C₂₉×C₆₁	D₃	1	1	yes	characteristic
4	C₂₉×D₆₁	—	9	1	no	Hall
5	C₂₉×C₆₁	D₉	1	1	yes	characteristic, complemented, Hall
6	D₅₄₉	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₉×C₆₁	C₂×C₂₉	1	1	yes	characteristic, complemented, Hall
8	D₉×C₂₉	—	61	1	no	maximal, Hall
9	D₁₈₃	—	3	1	no	—
10	C₉×C₂₉	D₆₁	1	1	yes	characteristic, complemented, Hall
11	C₃×C₆₁	D₃×C₂₉	1	1	yes	characteristic
12	D₃×C₂₉	—	183	1	no	—
13	D₆₁	—	9	1	no	Hall
14	C₃×C₂₉	D₁₈₃	1	1	yes	characteristic
15	C₆₁	D₉×C₂₉	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₂₉	—	549	1	no	Hall
17	C₂₉	D₅₄₉	1	1	yes	characteristic, direct product factor, Sylow
18	D₉	—	61	1	no	Hall
19	C₉	C₂₉×D₆₁	1	1	yes	characteristic, complemented, Sylow
20	D₃	—	183	1	no	—
21	C₃	C₂₉×D₁₈₃	1	1	yes	characteristic
22	C₂	—	549	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₂₉	D₅₄₉
commutator, cosocle, hypocenter	C₉×C₆₁	C₂×C₂₉
Frattini	C₃	C₂₉×D₁₈₃
Fitting	C₉×C₂₉×C₆₁	C₂
socle	C₃×C₂₉×C₆₁	D₃
LCS	G ▷ C₉×C₆₁
UCS	C₁ ◁ C₂₉

Splittings G = N ⋊ H with N normal; H ≅ G/N.

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.